package datastructure.book.dp._1_pathway.exercise.first;

public class _3_Solution {
    /**
     * 给定一个包含非负整数的 m x n 网格 grid ，
     * 请找出一条从左上角到右下角的路径，使得路径上的数字总和为最小。
     * 说明：每次只能向下或者向右移动一步。
     * 例如：grid = [
     *                  [1,3,1],
     *                  [1,5,1],
     *                  [4,2,1]]
     * 1→3→1→1→1 的总和最小。输出：7
     * m == grid.length
     * n == grid[i].length
     * 1 <= m, n <= 200
     * 0 <= grid[i][j] <= 200
     */
    public int minPathSum(int[][] grid) {
        int m = grid.length;
        int n = grid[0].length;
        int[][] f = new int[m][n];
        f[0][0] = grid[0][0];
        for (int i = 1; i < n; i++) {
            f[0][i] = f[0][i-1]+grid[0][i];
        }
        for (int i = 1; i < m; i++) {
            f[i][0] = f[i-1][0]+grid[i][0];
        }
        for (int i = 1; i < m; i++) {
            for (int j = 1; j < n; j++) {
                f[i][j] = Math.min(f[i-1][j],f[i][j-1])+grid[i][j];
            }
        }
        return f[m-1][n-1];
    }
    public int minPathSum2(int[][] grid) {
        int m = grid.length;
        int n = grid[0].length;
        int[] f = new int[n];
        f[0] = grid[0][0];
        for (int i = 1; i < n; i++) {
            f[i] = f[i-1]+grid[0][i];
        }
        for (int i = 1; i < m; i++) {
            for (int j = 0; j < n; j++) {
                if (j - 1 >= 0) {
                    f[j] = Math.min(f[j - 1], f[j]) + grid[i][j];
                } else {
                    f[j]+=grid[i][j];
                }

            }
        }
        return f[n-1];
    }
}
